Answer Happy

PLEASE SOLVE NO (iii)...!!
Posting seperately for (IV)
1. Compute the interpolating polynomial through the points (-3,4), (-2,-2), (-1,2) using hand cal- culations with the following methods. (i) Lagrange interpolation. (ii) Newton interpolation. (iii) Natural spline. You may take your starting point to be the cubic spline interpolating function, M; Mj+1 M;h; M;+1 h; – x)3 + S;(x) (2 c – x;)3 (2j+1 – 2 (C- – x;) 6 h; 6 h; 6 6 Yj (Xj+1 - x) + X;) (L;+1 yj+(r hj on each interval x € [Ej, Lj+1]. (iv) Cubic spline with derivative conditions S/(-3) = 5, S:(-1) = 2. Your starting point can be the appropriate equation in (iii) where the derivatives are involved. (v) Use Matlab to confirm your results and plot a figure showing all curves. Include your code and the figure in your submission - an example of such a plot is shown below.